This contract is part of a clinical trial of T cell-depletion in unrelated donor bone marrow transplantation. The primary objective of the clinical trial is to determine if a reduction in morbidity and mortality from acute and chronic graft versus host disease (GvHD) can be achieved in patients given T cell-depleted marrow from an unrelated donor without a counterbalancing increase in relapse of leukemia and graft failure. This prospective clinical trial will require a total of 560 patients, randomized to T cell- depletion or no depletion of their graft. Two important components of this study are to characterize the numbers and types of cells in the graft, and to monitor immune reconstitution. This project includes a medical coordinating center and four therapy groups. The medical coordinating center is staffed by biostatisticians, an immunologist, computer programmers, and research coordinators. The medical coordinating center will make randomized treatment assignments, collect and monitor the data, analyze the results, and produce summary reports. The study is expected to last seven and one-half years.